In this paper I present a problem for the conventionalist regarding temporal metrics, and I defend an objectivist position on the ground of its explanatory force. Roughly, the conventionalist has it that there is no fact of the matter with respect to the truth or falsity of judgments of the kind “event e1 lasted as long as event e2”, while the objectivist thinks that they are grounded in objective features of space-time. I argue that, by positing grounds for judgments of relative temporal length, the objectivist gains an explanatory force that the conventionalist position lacks.
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Note that the otherwise interesting philosophical debate on whether the relation between the structure of the order of the purely temporal elements “containing” the events and the structure determined by the temporal relations between events is identity — viz. the relationist vs. substantivist debate — will not concern us.
Of course, it is a consequence of STR that such mappings are always relative to a reference system — for instance, the one centred on the instrument — assumed to be at rest or in inertial motion. Relativistic considerations are immaterial to the problem that I am discussing in what follows (although the objectivist position that I eventually defend can be easily extended to a relativistic environment).
Adolf Grünbaum, a proponent of conventionalism who does not generally show much sympathy for metaphysical debates, seems to agree: “clearly [...] the thesis of the conventionality of congruence [i.e. of temporal metrics] is, in the first instance, a claim concerning structural properties of physical space and time [...]” (Grünbaum 1963: 26)
A slightly stronger version of objectivism may have it that temporal length properties of events — their covering a certain “amount of time” — are genuine properties. This stronger version entails the weaker version. I confine my discussion to the weaker version here, because the stronger version raises problems about dense and continuous structure and objective metrical properties, which are beside the point for the problem that I want to discuss (See Newton-Smith 1980: 166). Again, relativistic considerations are bracketed here. Besides, it may have occurred to the attentive reader that an analogous skeptical scenario holds for spatial length measurements with physical rulers. I do not need here to enter the difficul issue on whether there are interesting epistemic differences between the spatial and the temporal case. However, although I will ingnore the spatial case althogether, the objectivist position that I defend at the end suggests that from a metaphisical standpoint the two cases are analogous (given special relativity).
It is very important to note that preservation of mutual congruence among cognate clocks is not observational evidence for congruence between the events produced in succession by each clock. Even if we had billions of clocks ticking in unison, we cannot rule out the possibility that the intervals produced in succession by each clock are not isochronic. See (Le poidevin 2007: 115).
On super-valuationism, see Varzi 2007.
A general feature of supervaluationist semantics is that theorem-hood is preserved, thus if the underlying logics is classic, any classically valid sentence is true in any supervaluation.
Of course, if it is true that, intuitively, there are super-false atomic judgements in L, a different choice of primitive would have given us immediately super-true judgments in L. What I am claiming here is that even if we admit only “natural” primitives in L (i.e., those that respect our intuitions with respect to crazy claims such as “My last heartbeat lasted as much as the Ice Age”), it is not unreasonable to maintain that we have super-true atomic statements.
Incidentally, if the boundaries between scientific theories and philosophical ones are not clear cut, as it is also reasonable to believe, theoretical considerations can also play a role in evaluating incompatible scientific theses. An analogous thesis is defended at length by (Psillos 2009).
Grünbaum, A. (1963). Philosophical problems of space and time. New York: Knopf.
Le Poidevin, R. (2007). The images of time. Essay in Temporal Representation. Oxford: Oxford University Press.
Nerlich, G. (1994). What spacetime explains. Cambridge: Cambridge University Press.
Newton-Smith, W. H. (1980). The structure of time. London: Routledge.
Psillos, S. (2009). Knowing the structure of nature: essays on realism and explanation. Palgrave-MacMillan.
Reichenbach, A. (1950). The philosophy of space and time. New York: Dover Publications.
Varzi, A. (2007). Supervaluationism and its logic. Mind, 116, 633–676.
For helpful comments and discussions thanks to an anonymous referee and to the participants of the “Rome-Barcelona Workshop in the Philosophy of Science” (University of Roma III, May 2013). Thanks to the projects FFI2011-29560-C02-01, FFI2011- 25626, and CSD2009-00056 of the Spanish Ministerio de Ciencia e Innovacion (MICINN) for financial supports.
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Torrengo, G. Chronometric Explanations. Philosophia 44, 275–287 (2016). https://doi.org/10.1007/s11406-015-9669-4
- Temporal metric